We consider the Potts model on a hierarchical lattice. A multifractal analysis of the Julia set associated with the renormalization-group transformation, which gives the Fisher zeros of the partition function in the complex temperature plane, is performed. The behavior of the singularity...

We have studied two generalized Frenkel-Kontorova (FK) models. In one of them the interatomic potential is changed from simple harmonic to Toda; in the other the external potential is changed from sinusoidal to nonanalytic. Their critical behaviors are found to be markedly different. In the Toda...